Bob Geldof has said his family are “beyond pain” following the death of his daughter Peaches at the age of 25.
Ms Geldof, second daughter of musician Bob Geldof and the late TV presenter Paula Yates, was found dead at her home in Wrotham, Kent, on Monday.
Kent Police said the death was being treated as “non-suspicious but unexplained and sudden”.
Ms Geldof, who had two young sons with her second husband, musician Tom Cohen, was 11 when her own mother died.
Bob Geldof said in a family statement: “She was the wildest, funniest, cleverest, wittiest and the most bonkers of all of us.
“Writing ‘was’ destroys me afresh. What a beautiful child. How is this possible that we will not see her again? How is that bearable?
“We loved her and will cherish her forever. How sad that sentence is. Tom and her sons Astala and Phaedra will always belong in our family, fractured so often, but never broken.”
The statement was signed Bob, Jeanne, Fifi, Pixie and Tiger Geldof.
Born in 1989, Peaches Honeyblossom Geldof embarked on a media career at the age of 15 when she began writing a column for Elle magazine.
She left home at 16 and went on to contribute to the Daily Telegraph and the Guardian, as well as TV shows including ITV2’s OMG! with Peaches Geldof.
She also worked as a model and, just last week, attended a launch for Tesco’s F&F clothing range in London.
Paula Yates’s death came after she split with Bob Geldof and formed a relationship with INXS frontman Michael Hutchence, who then died in 1997.
Ms Geldof was previously married to rock musician Max Drummey but the pair separated in 2009 after a six-month marriage.
She leaves her husband and sons; father Bob Geldof; sisters Fifi Trixibelle and Pixie; and younger half-sister, Tiger Lily Hutchence Geldof.